In general, a resonator for a rate gyro or a free gyro comprises a hemispherical bell provided with a central stem that is fastened to a bell support part. The bell is made of an electrically-insulating material and is uniformly coated in an electrically-conductive layer so as to define electrodes at a peripheral edge of the bell, which electrodes face electrodes on a support part. The electrodes are powered to cause the bell to be deformed into an ellipse and in order to detect the orientation of the ellipse. The material used for the bell is generally silica that guarantees accuracy for the sensor by virtue of very low intrinsic damping. The conductive layer is generally made of metal, but presents the drawback of conferring both mechanical damping and electrically damping (as a result of the resistive losses produced by detection current flowing in the conductive layer in the vicinity at the equator). The quality of the resonator is thus highly influenced by the conductive layer. The damping of the vibrations also makes it necessary to increase the energy for sustaining vibration, and above all it degrades the performance of the resonator by increasing drift if the resonator presents a geometrical harmonic defect of order four.